Can a net propulsive effect occur between phase shifted antennae?

So this question centers around an electromagnetic thought experiment suggested by the patent titled "Efficient RF electromagnetic propulsion system with communications capability", US8459002B2. The critical part is these paragraphs:

Consider two short parallel wires (a and b as in FIG. 2A) in air or a vacuum, fixed relative to each other and separated by a distance of one meter. Further, suppose that each is carrying a constant (DC) current that is flowing in the same direction. As a result of the magnetic fields generated by the currents, a force is generated between the two wires that attracts each to the other. These forces are equal but in opposite directions, resulting in a zero net force on the system of wires. The total force on this system is balanced.

Now, let us replace the DC current with an alternating current (see FIG. 2B) that has a frequency of c/4 Hertz (“c” being the speed of light; c/4 Hz, =74.9 MHz). Also let the relative phase of the two currents be offset by 90 degrees, with the phase of a leading that of b (121 and 122). Because of the propagation delay from a to b (as illustrated in FIG. 2 b), an observer at b observing the magnetic field from a would say the two currents are in phase (121 b and 122 b), thus wire b is attracted towards a. On the other hand, an observer at a would say that the phases are off by 180 degrees (121 a and 122 a), resulting in a repulsive force on wire a. As a result, an upwards force is exerted on each wire creating an unbalanced system. If the phase of b led that of a, then the forces would be downwards.

So the concept of the 90 degree phase shift between two excited antennae producing an effect where one antenna "sees" the field not shifted and the other sees it 180 degrees out of phase makes sense, but what about the idea of a net propulsive effect? It seems like it's clear that there would be no net force because one wire would try to attract them together and the other would push them apart, with the forces balancing out and resulting in no motion, but the part that's confusing me is the following. Does it make sense that if one wire antenna reacts to the field emitted by the other wire in such a way that it's attracted to the field, does that also mean that the other wire is attracted even if the attractive field has already been emitted? I think that would mean that the field emitted is anchored to the momentum of the wire/antenna, so that the two wires both move in one direction when the EM fields reach each other, but then a back reaction occurs through the field which causes the wires to move in the opposite direction, pushing them back in the opposite direction so there's no net movement (the wires shift together in one direction then back in the opposite cycle after cycle). So the push-back force would be offset 90 degrees but cancel out any net motion. Does this explanation make sense?

1 Answer

Trying to analyze what's going on in the induction zone of a multi element antenna is a tricky business: you can't assume the field is like a static field.

However, in this case, the problem is pretty easy when you realize that in the far field you just have the superimposed fields of the two elements. The momentum carried by the far field radiation tells you the force on the antenna.

For a practical implementation, the force is small but not zero. This configuration is directional: it's sometimes known as a "cardioid" antenna, although the pattern is more complicated than a simple cardioid. It has a very broad beam, so it won't have quite as much thrust as a highly directional antenna radiating the same power.

But it's just an antenna, thrusting via ordinary radiation pressure. There is no magic.

• So a low efficiency photon rocket? Commented Aug 31, 2022 at 15:32
• @GrapefruitIsAwesome Yes. Not terribly low. Commented Aug 31, 2022 at 15:36
• @JohnDoty I apologize for taking some time before marking or responding to your answer but I wanted to see if there would be other approaches. Even though what you said seems to make sense, I don't quite get how it wouldn't produce a force much larger than that from radiation pressure (like a force on the order of what you'd get if wires were pulling together). Are you saying that once the electromagnetic field radiates, the forces it can exert on nearby conductors with current are significantly reduced? I'm not saying your answer is wrong, I'm just saying my understanding isn't cleared up.
– Tom
Commented Sep 10, 2022 at 18:08
• @Tom The oscillatory forces on the structure are indeed much larger than the net radiation pressure. However, the field structure in the induction zone isn't simple, and does not reflect your static analysis. Electric fields are very important. This isn't easy math at all: get a textbook on antenna theory and prepare for a heavy slog. On the other hand: we have great confidence that momentum is conserved, so if you have thrust it must be reflected in the momentum (radiation pressure) of the outgoing radiation in the far field. Commented Sep 10, 2022 at 18:20